There is no law regarding bank accounts ... you can have one on any visa or no visa at all. It is just rules made up by the mother bank or the bank branch.
I would consider to buy a new Laptop here. Depending if you can store your old PC "at home". Da es hier keine Urheberrechtsabgaben auf SSD etc. gibt, sind die Laptops super billig. Lenovo Thinkpad z.B. Allerdings weiss ich natuerlich nicht, was fuer einen Boliden Du hast, und was fuer Rechenpower Du brauchst.
Anonymous participant Depending on your company it makes perhaps more sense to look into an LTR (so called smart visa). For remote work under an DTV you do not need a work permit.